Math Problem Statement

determine the linear correlation coefficient between commute time and well-being score. round to the decimal places as needed.

Determine the linear correlation coefficient between commute time and well-being score. Round to the decimal places as needed.

Solution

import pandas as pd from scipy.stats import pearsonr

Data extracted from the image

data = { "Commute Time (in minutes)": [5, 13, 24, 35, 53, 71, 99], "Well-Being Score": [69.5, 68.5, 67.4, 67.3, 66.2, 65.8, 63.3] }

Create a DataFrame

df = pd.DataFrame(data)

Calculate the Pearson correlation coefficient

correlation_coefficient, _ = pearsonr( df["Commute Time (in minutes)"], df["Well-Being Score"] )

correlation_coefficient_rounded = round(correlation_coefficient, 3) correlation_coefficient_rounded-0.981-0.981successThe linear correlation coefficient between commute time and well-being score is approximately -0.981. This indicates a strong negative correlation, meaning as commute time increases, well-being scores tend to decrease.

Would you like further details or explanations?

Here are 5 related questions you might consider:

  1. How can the strength of this correlation be interpreted in a practical scenario?
  2. Is this correlation enough to infer causation between commute time and well-being?
  3. What would be the effect of outliers on this correlation coefficient?
  4. How could we use regression to predict well-being scores based on commute times?
  5. What are other factors that could affect well-being in addition to commute time?

Tip: Always visualize your data (e.g., scatterplot) to better understand the relationship beyond the correlation coefficient!

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation
Linear Relationship

Formulas

Pearson correlation coefficient formula

Theorems

Correlation properties in statistics

Suitable Grade Level

Grades 10-12